The surface area of the balloon is
.
Differentiate both sides with respect to an arbitrary variable representing time:
Meanwhile, the volume of the balloon is
.
Differentiating with respect to
yields
You're told that, at the point when the radius
, the volume of the balloon increases at a rate of
, which means
. Use this to solve for the rate of change of the radius,
.
Substitute this into the equation for the rate of change of the surface area and solve for
.
Answer:
The answer is 21
Step-by-step explanation:
- Male the shapes look similar by turning the smaller to be the same as the bigger one the compare side and then find x
Given:
The figure of a trapezoid.
To find:
The image points of the given figure after rotation of 180 degrees.
Solution:
From the given figure, it is clear that the vertices of the trapezoid are W(-4,2), X(-3,4), Y(-1,4), Z(0,2).
If a figure is rotated 180 degrees about the origin, then
Using this rule, we get
Therefore, the image points are W'(4,-2), X'(3, -4), Y'(1, -4), Z'(0, -2). So, the correct option is 1.
Let a and c represent the numbers of adult and children's tickets sold, respectively. The system of equations will have one equation for revenue and one equation for number of tickets.
The revenue equation is
18a +9c = 4959
The number of tickets equation is
a + c = 319
_____
The solution can be found any number of ways. It is
(a, c) = (232, 87)
Answer:
24
Step-by-step explanation:
We are given the logarithmic expression:
We are also given by the problem that:
From the expression, we will simplify it using two properties:
Therefore, apply the properties to simplify:
Next, we will use another property to take an exponent as a coefficient:
Hence:
Substitute what are given in the problem and the answer will be:
Hence, the answer is 24.